Figure 3

Two examples of how genetic homophily affects the evolutionary dynamics in our model, showing possible trajectories of cooperation as human homophily (tendency to interact with genetically related others) decreased over time due to changing social environments (blue lines). The evolutionary dynamics separates into qualitatively different regimes depending on the homophily level: \(h < {\hat{h}}\), Cooperators cannot persist (dark shading); \(h < h_1\), Defectors can both invade and persist (red shading); \(h > h_0\), Cooperators can invade (blue shading). In the human ancestral past (e.g., \(>1.6\) Ma³³), homophily was high (point A), which under the model would have allowed cooperation to invade (B). As interactions with nonkin increased (h decreased), Cooperation persisted even into the region where it could not invade (C). Depending on the parameter values, Cooperation can either persist even if homophily disappears entirely (i.e., all interactions become nonkin; D) or be lost below a certain level of homophily (E). The example illustrated uses the members-recruit group-formation model (\(h \equiv 1-q\)) with parameter values \(n=8\), \(W=2\), \(Y=3\), \(Z=0\); (a) \(\tau =5\), \(X=-1\); (b) \(\tau =4\), \(X=-0.5\). See Supplementary S5 for qualitatively similar results from other group-formation models and for sigmoid PGGs.